Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×C4×C13 | C2 | semidirect |
| 2. C2×C3×C22⋊D13 | C2 | semidirect |
| 3. C3×#6127 | C2 | direct (N × H) |
| 4. C2×C3×D52 | C2 | semidirect |
| 5. C2×C3×C4×D13 | C2 | semidirect |
| 6. C2×C3×Dic26 | C2 | semidirect |
| 7. C2×#6127 | C3 | direct (N × H) |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 13. C3×C22⋊D13 | C22 | semidirect |
| 15. C3×D52 | C22 | semidirect |
| 16. C3×C4×D13 | C22 | semidirect |
| 17. C3×Dic26 | C22 | semidirect |
| 18. C22×C4×C13 | C2×C3 | semidirect |
| 19. C2×C22⋊D13 | C2×C3 | semidirect |
| 20. #6127 | C2×C3 | direct (N × H) |
| 21. C2×D52 | C2×C3 | semidirect |
| 22. C2×C4×D13 | C2×C3 | semidirect |
| 23. C2×Dic26 | C2×C3 | semidirect |
| 36. C2×C4×C13 | C22×C3 | semidirect |
| 37. C22⋊D13 | C22×C3 | semidirect |
| 39. D52 | C22×C3 | semidirect |
| 40. C4×D13 | C22×C3 | semidirect |
| 41. Dic26 | C22×C3 | semidirect |
| 44. C2×C3×C13 | #41 | semidirect |
| 60. C22×C3×C4 | D13 | semidirect |
| 61. C3×C13 | C2×#41 | semidirect |
| 64. C2×C13 | C3×#41 | semidirect |
| 76. C2×C3×C4 | C2×D13 | semidirect |
| 82. C22×C4 | C3×D13 | semidirect |
| 83. C13 | C2×C3×#41 | semidirect |
| 101. C2×C4 | C2×C3×D13 | semidirect |
| 104. C2×C3 | #6127 | direct (N × H) |
| 114. C3 | C2×#6127 | direct (N × H) |
| 117. C2 | C3×#6127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C13 | 2 |
| C2×C3×C22⋊D13 | 2 |
| C3×#6127 | 2 |
| C2×C3×D52 | 2 |
| C2×C3×C4×D13 | 2 |
| C2×C3×Dic26 | 2 |
| C2×#6127 | 3 |
| C2×C3×#41 | 13 |